Decomposition of Lagrangian classes on K3 surfaces
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Published version
Date
2020
DOI
Authors
Lai, Kuan-Wen
Lin, Yu-Shen
Schaffler, Luca
Version
OA Version
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Citation
Kuan-Wen Lai, Yu-Shen Lin, Luca Schaffler. 2020. "Decomposition of Lagrangian Classes on K3 Surfaces." preprint, arXiv: 2001.00202, https://arxiv.org/abs/2001.00202
Abstract
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in terms of lattice theory. As a result, we prove the decomposability on an arbitrary K3 surface with respect to the Kähler classes in dense subsets of the Kähler cone. Using the same technique, we show that the Kähler classes on a K3 surface which admit a special Lagrangian fibration form a dense subset also. This implies that there are infinitely many special Lagrangian 3-tori in any log Calabi-Yau 3-fold.